Question 151539
Since the "lenght of a rectangular garden is 20 feet longer than the width", this means that {{{L=W+20}}}



{{{P=2W+2L}}} Start with the perimeter equation.



{{{P=2W+2(W+20)}}} Plug in {{{L=W+20}}}



{{{P=2W+2W+40}}} Distribute



{{{P=4W+40}}} Combine like terms.



Since the "perimeter must be between 80 and 100 feet", this means that {{{80<=P<=100}}}



{{{80<=P<=100}}} Start with the given compound inequality.



{{{80<=4W+40<=100}}} Plug in {{{P=4W+40}}}



{{{(80)/4<=w<=(100)/4}}} Divide all sides by 4.



{{{20<=w<=25}}} Reduce.



{{{80-40<=4w<=100-40}}} Subtract {{{40}}} from all sides.



{{{40<=4w<=100-40}}} Combine like terms on the left side.



{{{40<=4w<=60}}} Combine like terms on the right side.



{{{(40)/4<=w<=(60)/4}}} Divide all sides by 4.



{{{10<=w<=15}}} Reduce.



So our answer is {{{10<=w<=15}}} which means that the width must be between 10 and 15 feet.